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Complex numbers are an intrinsic part of the mathematical formalism of quantum theory and are perhaps its most characteristic feature. In this article, we show that the complex nature of the quantum formalism can be derived directly from the assumption that a pair of real numbers is associated with each sequence of measurement outcomes, with the probability(More)
Quantum theory is a probabilistic calculus that enables the calculation of the probabilities of the possible outcomes of a measurement performed on a physical system. But what is the relation of this probabilistic calculus with probability theory itself? For instance , is quantum theory compatible with probability theory? If it is compatible, does it extend(More)
General theoretical principles that enable the derivation of prior probabilities are of interest both in practical data analysis and, more broadly, in the foundations of probability theory. In this paper, it is shown that the general rule for the assignment of priors proposed by Jeffreys can be obtained from, and is logically equivalent to, an intuitively(More)
The operational formalism to quantum mechanics seeks to base the theory on a firm foundation of physically well-motivated axioms [1]. It has succeeded in deriving the Feynman rules [2] for general quantum systems. Additional elaborations have applied the same logic to the question of identical particles, confirming the so-called Symmetrization Postulate(More)
Hair cells, which detect and encode sound stimuli, have been shown to have a non-linear response and self sustaining oscillations. Here, we look at the Van der Pol oscillator, which has these properties, and numerically calculate its response to multiple driving frequencies. Any nonlinear system's response to multiple driving frequencies will have not just(More)
Quantum theory poses deep challenges to the mechanical conception of reality that underlies classical physics. Yet today, over eighty years after its creation, its implications for our picture of reality remain enshrouded in uncertainty. In view of the current search for a more comprehensive theory of physics (a so-called theory of everything), it is vital(More)
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